1590s, "a sending abroad" (as an agent), originally of Jesuits, from Latin missionem (nominative missio) "act of sending, a dispatching; a release, a setting at liberty; discharge from service, dismissal," noun of action from past-participle stem of mittere "to release, let go; send, throw," which de Vaan traces to a PIE *m(e)ith- "to exchange, remove," also source of Sanskrit methete, mimetha "to become hostile, quarrel," Gothic in-maidjan "to change;" he writes, "From original 'exchange', the meaning developed to 'give, bestow' ... and 'let go, send'."
Meaning "an organized effort for the spread of religion or for enlightenment of a community" is by 1640s; that of "a missionary post or station" is by 1769. The diplomatic sense of "body of persons sent to a foreign land on commercial or political business" is from 1620s; in American English, sometimes "a foreign legation or embassy, the office of a foreign envoy" (1805).
General sense of "that for which one is sent or commissioned" is from 1670s; meaning "that for which a person or thing is destined" (as in man on a mission, one's mission in life) is by 1805. Meaning "dispatch of an aircraft on a military operation" (by 1929, American English) was extended to spacecraft flights (1962), hence, mission control "team on the ground responsible for directing a spacecraft and its crew" (1964). As a style of furniture, said to be imitative of furniture in the buildings of original Spanish missions to western North America, it is attested from 1900.
"relating to or pertaining to a mission, sent on a mission," especially a Christian mission, 1640s, from Modern Latin missionarius "pertaining to a mission," from Latin missionem (see mission).
by c. 1500, "a written message sent by superior authority; a commandment," noun use of the adjective (mid-15c.) meaning "sent by superior authority" (in phrase lettres missives) from Medieval Latin missivus "for sending, sent," especially in littera missiva "letters sent," from Latin missus, past participle of mittere "to send" (see mission).
1610s, "allowable," from French admissible, from past participle stem of Latin admittere "allow to enter, admit, give entrance," from ad "to" (see ad-) + mittere "let go, send" (see mission). Meaning "capable of being allowed entrance" is from 1775; specific sense of "capable of being used in a legal decision or judicial investigation" is recorded from 1849.